The curve \( y(x)=a x^{3}+b x^{2}+c x+5 \) touches the \( x \)-axis at the point \( P(-2,0) \) a... VIDEO
The curve \( y(x)=a x^{3}+b x^{2}+c x+5 \) touches the \( x \)-axis at the point \( P(-2,0) \) and cuts the \( y \)-axis at the point \( Q, y^{\prime} \) is equal to 3 . Then the local maximum value of \( y(x) \) is
(a) \( \frac{27}{4} \)
(b) \( \frac{29}{4} \)
(c) \( \frac{37}{4} \)
(d) \( \frac{9}{2} \)
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